(553f) Machine Learning for Predicting Pitzer Parameters Based on Ion Specific Properties

The use of technology metals in the ICT sector has increased tremendously since the 1990s. Improved efficiency, cameras, touchscreens, and wireless connectivity have been achieved by innovative usage of different elements. In 1990, the manufacturing of computers and mobile phones used approximately 10 metals. Now the number exceeds 50. The fractionation, concentration, recovery and refining of these elements require fundamental material property data, particularly so for their mixtures appearing in the respective extraction processes. Although much of the fundamental property measurements were conducted in the first half of the twentieth century, there are still many metals and ion pairs for which there is too little experimental data available, thus hampering the development of new process concepts. Conduction of such fundamental measurements with conventional techniques is elaborate and time-consuming, which has led to scarce practicing in this field .Therefore, possibilities for extending the current thermodynamic database (such as [1]) are limited and development of new process concepts for refining the increasing number of elements becomes more difficult.

The exponential growth of computational power has introduced new possibilities for computational science. Data-based machine learning algorithms have been developed and deployed to many impressive solutions, such as computer games, machine vision, and drug discovery. The aim of this study is to evaluate whether these new machine learning algorithms can be applied for predicting fundamental property data of ion pairs in aqueous solutions. Such property data would be vital for developing practical applications in hydrometallurgy, water purification, and the treatment of industrial concentrates and brines.

Methodology

Mean activity coefficients of cation-anion pairs in aqueous solution were predicted using a neural network trained on data from [2]. This data describes Pitzer parameters [3] for calculating mean activity coefficients for over 200 different cation-anion pairs covering 50 different cations and 54 different anions. The parameter set was considered as proxy for a evaluated experimental data within the stated validity range, which varied but in most cases extended up to 6 M. Mean activity coefficients acted as labels (outputs) for the neural network. These labels were connected to features (inputs) of each particular cation and anion. The features included i) molecular weight, ii) charge, iii) hydratation number, iv) enthalpy of hydratation, v) entropy of hydratation, vi) Gibbs’ energy of hydratation, vii) softness, viii) partial molar volume, and ix) radius. The x) molality was used as an additional input for the neural network. The size of dataset was approximately 5000 data points. 80 % of the data was used for training and the remaining part for validation.

Based on preliminary screening of different neural network structures, a feed-forward neural network was chosen. It suited better for estimating continuous mean activity coefficients as functions of molality compared to e.g. regression trees. Machine learning studies were conducted using the Keras [4] framework as it allows rapid development of neural network based models. Tensorflow [5] and PlaidML [6] were used as Keras backends. The hyper-parameters of the neural network model were optimised using the Scikit-learn [7] toolbox. Model development was conducted using the Jupyter [8] notebook environment within the Anaconda [9] Python toolbox. Calculations were run on a laptop computer (Windows 10, Intel quad core, 1900 MHz) with separate graphics processing unit (AMD Radeon RX550).

Results

The model for predicting mean activity coefficients was divided into two parts. The first part described an average mean activity coefficient based solely on the charge of the cation and the charge of anion (1-1,1-2, 2-1,2-2,1-3,3-1,4-1,5-1). The second part represented the deviation of the mean activity coefficient for a specific cation-anion pair with respect to the average mean activity coefficient for ions of corresponding charges. This deviation was estimated based on the neural network model trained using above mentioned cation-anion specific features and labels obtained from literature.

The over-fitting of the neural network model was avoided using hyper-parameter optimisation. The following hyper-parameters were optimised: i) number of epochs, ii) batch size, iii) applied activation function, iv) number of neurons in each layer, v) number of hidden layers, vi) loss function, and vii) training algorithm. Based on the optimisation of hyper-parameters, it was concluded that a two hidden layer network topology with about 20 neurons in the first layer and about 5 neurons in the second layer was sufficient. A special characteristic of this feed-forward neural network topology was the fact that molality was fed as a feature to both layers. Other features were supplied only to the first layer of network. This allowed accurate modelling of diluted suspensions as described by Debye-Hückel limiting law [10].

80% of the data was used for training and 20% for model validation. The accuracy of predicting mean activity coefficients using the final neural network model was improved for 65% of the cation-anion pairs when compared to charge specific average values. The model failed to improve accuracy in cases were the original data for certain anions were scattered. Some polyatomic organic anions were only participating in one or two ion pairs. In addition, some features used for machine learning were not defined for these polyatomic organic anions. On the other hand, predicting mean activity coefficients for cation-anion pairs with inorganic anions (such as SO₄, CO₃, NO₃) was successful in many cases.

Summary

Machine learning was applied for predicting mean activity coefficients for ion pairs in concentrated aqueous solutions. A two-layer feed-forward neural network model was selected. Ion specific parameters were used as features of the model. Labels of the model was mean activity coefficient for each cation-anion pair. The developed model was able to improve the predicted mean activity coefficients for two thirds of the cases compared to using only ion charges for prediction. Predictions were most successful when modelling metal cations and inorganic anions. The training data for polyatomic organic anions was too scarce.

The future studies include: i) the verification of developed model against another independent data set, ii) the collection of a larger database for training, iii) the utilisation of original measurement data for training, iv) the rigorous analysis of the most important features (inputs), and v) the development of a practical tool for predicting Pitzer parameters for those cation-anion pairs where no measurement data is available.

The presented methodology might be used when developing new processes related to circular economy. It might provide a rapid tool for screening concepts prior to conducting experiments or measuring material properties for previously unknown cation-anion pairs.

References

[1] Pajarre, R., Koukkari, P. and Kangas, P., Industrial and mine water chemistry - Advanced aqueous database for modelling industrial processes, VTT Technol. 321 (2018).

[2] Pitzer, K.S. and Mayorga, G., "Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent", J. Phys. Chem., 77(19):2300–2308 (1973).

[3] Pitzer, K.S., ed., Activity coefficients in electrolyte solutions, 2nd ed., CRC Press, Boca Raton, FL (1991).

[4] Chollet, F. and others, Keras, (2015).

[5] Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., et al., TensorFlow: Large-scale machine learning on heterogeneous systems, (2015).

[6] plaidML, plaidML, (2019).

[7] Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., et al., "Scikit-learn: Machine Learning in Python", JMLR, 12:2825−2830 (2011).

[8] Kluyver, T., Ragan-Kelley, B., Pérez, F., Granger, B., Bussonnier, M., Frederic, J., et al., "Jupyter Notebooks – a publishing format for reproducible computational workflows", In: Positioning and Power in Academic Publishing: Players, Agents and Agendas, F. Loizides and B. Schmidt (Eds.), IOS Press, (2016).

[9] Anaconda, Anaconda Software Distribution. Computer software, (n.d.).

[10] Huckel, E. and Debye, P., "Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen", Phys. Zeitschrift, 25(1924).